Measurement Uncertainty in Clinical Laboratory: Step by Step

Measurement uncertainty (MU) in the clinical laboratory is a quantitative statement of doubt about a result: a glucose of 126 mg/dL with an expanded uncertainty of ± 6.2 mg/dL means the true value is expected, with about 95 % confidence, to lie between roughly 120 and 132 mg/dL. ISO 15189 asks medical laboratories to estimate the uncertainty of their measured quantity values and to review it, and assessors often ask to see the calculation for a few analytes. This guide works through one glucose example from raw internal QC and EQAS numbers to the reported "±" value using the widely used top-down approach, checks every step, and adds the Sigma metric from the same data.

Starter content. The method below is one accepted approach, consistent with ISO/TS 20914:2019 and Nordtest-style guidance. Your laboratory chooses and documents its own approach; follow the current NABL guidance applicable to medical laboratories. Calculations support, and do not replace, the judgement of your biochemist or pathologist.

What is measurement uncertainty in a medical laboratory?

No measurement is exact. Every result carries random error (imprecision: repeat measurements scatter) and possibly systematic error (bias: results run consistently high or low). Measurement uncertainty combines these into one number expressed as a standard uncertainty (one standard deviation) or, more usefully for reporting, an expanded uncertainty U that covers about 95 % of the likely values.

Why it matters: when a result sits close to a decision limit, such as HbA1c near a diagnostic cut-off, glucose near 126 mg/dL or creatinine near the upper reference limit, the uncertainty tells the clinician whether the difference from the limit is meaningful. It also tells the lab whether a method is fit for purpose.

MU versus total error. Total analytical error (TE) adds bias and imprecision linearly (for example TE = |bias| + 1.65 × CV) and is compared with an allowable total error (TEa). Measurement uncertainty, in the GUM tradition, combines components as a root sum of squares and, in principle, expects significant bias to be corrected. Clinical labs often use both: TE and Sigma for QC planning, MU for the uncertainty statement. They answer different questions, so do not mix their formulas.

Top-down vs bottom-up: which approach small labs use

A bottom-up approach lists every source of uncertainty (pipette volumes, calibrator values, temperature, reagent lot) and combines them. It is rigorous but impractical for a routine lab running dozens of analytes. A top-down approach uses data the lab already has: long-term internal QC captures most random variation over months, and EQAS or certified reference material results capture bias. Most medical laboratories use top-down. For a comparison of the formulas in use, see The top-down approach to measurement uncertainty: which formula should we use in laboratory medicine?, and for minimum requirements, the joint working group paper at PMC5696748.

What data you need

• Long-term IQC for each control level: ideally at least six months, and not fewer than about 20 in-control results per level, covering reagent and calibrator lot changes, different operators and routine maintenance. Exclude only results with a documented handling error.
• At least two EQAS results (or measurements of a certified reference material) for the analyte, with the assigned values.
• The uncertainty of the assigned value, u(Cref), if the EQAS provider or reference material certificate states it. If unknown, many labs set it to zero and say so.
• A medical decision level at which to express the result, for example glucose 126 mg/dL.

Step-by-step calculation

Illustrative example: glucose on a chemistry analyzer. The numbers are an example, chosen to be reproducible; they are not from a real laboratory.

Step 1: Imprecision u(Rw) from IQC CV (two levels pooled)

Over six months, the normal-level control has a mean of 92.4 mg/dL and an SD of 1.94 mg/dL, so CV = 1.94 ÷ 92.4 × 100 = 2.10 %. The high-level control has a mean of 285.0 mg/dL and an SD of 5.59 mg/dL, so CV = 1.96 %. Pooling the two levels as the root mean square: u(Rw) = √((2.10² + 1.96²) ÷ 2) = 2.03 %. (Some labs keep levels separate and use the level nearest the decision limit; either way, write the choice into the SOP.)

Step 2: Bias component from EQAS (RMS bias and u(Cref))

Three EQAS samples in the period: 111.7 vs assigned 110.0 mg/dL (bias +1.55 %), 96.6 vs 96.0 (+0.63 %) and 143.0 vs 141.0 (+1.42 %). The root mean square of the biases is RMS(bias) = √((1.545² + 0.625² + 1.418²) ÷ 3) = 1.26 %. The provider states the uncertainty of the assigned value as 0.5 %. Then u(bias) = √(RMS(bias)² + u(Cref)²) = √(1.264² + 0.5²) = 1.36 %.

Step 3: Combined standard uncertainty u_c

u_c = √(u(Rw)² + u(bias)²) = √(2.03² + 1.36²) = 2.44 %.

Step 4: Expanded uncertainty U = k × u_c (k = 2)

U = 2 × 2.44 = 4.89 %. The coverage factor k = 2 gives a confidence level of about 95 % for a normal distribution.

Step 5: Express it at a decision level (± mg/dL)

At 126 mg/dL: 126 × 4.89 ÷ 100 = ± 6.2 mg/dL, so a reported 126 mg/dL means about 119.8 to 132.2 mg/dL.

The formula from CV, in one line

U (%) = 2 × √( CV_IQC² + RMS(bias)² + u(Cref)² )

If the lab has no EQAS data yet and uses imprecision only, U = 2 × CV_IQC; for the example that would be 4.06 %, which understates the uncertainty because bias is ignored. That shortcut should be labelled as such.

Is my uncertainty acceptable?

A number alone does not say whether the method is good enough. Compare U with a maximum allowable measurement uncertainty the lab chooses and documents for each analyte, for example one derived from biological variation (a common approach sets the allowable standard uncertainty at a fraction of the within-subject biological variation) or a fraction of the TEa the lab uses for QC. If U exceeds the maximum, look first at the largest component: here imprecision (2.03 %) contributes more than bias (1.36 %), so tighter QC, maintenance or a method change would help more than a bias correction.

Bonus: the Sigma metric from the same numbers

The Sigma metric says how many standard deviations of the method fit inside the allowable error: Sigma = (TEa − |bias|) ÷ CV, all in percent. With an example TEa of 10 % (the lab chooses the TEa and its source, for example CLIA, biological variation or RCPA), the mean EQAS bias of 1.20 % and CV 2.03 %: Sigma = (10 − 1.20) ÷ 2.03 = 4.3. Labs sometimes use the RMS bias instead of the mean; with 1.264 % the result is (10 − 1.264) ÷ 2.03 = 4.30, the same to one decimal. By the conventional Six Sigma bands, 4 to 5 is "good": in the style of the Westgard Sigma Rules, a multirule QC procedure with about four control measurements per run is usually suggested at this level, while a method at 6 Sigma or more can run with simpler rules. Treat these as guidance for your QC plan, not automatic changes.

Measurement uncertainty statement template

Recalculate at least yearly, and whenever the method, analyzer or calibrator changes or a reagent lot verification shows a shift (see the lot to lot verification guide).

How PathLab Software calculates it every quarter

PathLab Software already stores your daily IQC runs (with Westgard rules) and EQAS results on the QC page. The Sigma & uncertainty tab calculates, for any period (default: the last three full months) and every active control target, n, mean, SD and CV; the bias from EQAS or from the target mean; the Sigma metric against the TEa your lab enters per analyte with its source label; and the top-down uncertainty with u(Rw), RMS bias, u(Cref), u_c, U and the ± value at a decision level you set. The formulas are shown on screen, results are flagged when there are fewer than 20 runs or fewer than two EQAS results, a method decision chart plots every analyte, and the measurement uncertainty statement prints for the quality file. It is part of the QC statistics module, included in the Complete and Network plans (pricing). The same QC data also feeds the analytical indicators on the quality indicators dashboard. PathLab Software supports the records NABL assessors commonly ask for; your accreditation is yours to obtain.

Get uncertainty and Sigma per analyte from your own QC every quarter: start a free trial.

Questions people ask

How do you calculate measurement uncertainty in a clinical laboratory?

With the top-down approach: take the long-term IQC CV as u(Rw), combine the RMS of EQAS biases with the uncertainty of the assigned value as u(bias), calculate u_c = √(u(Rw)² + u(bias)²), and report the expanded uncertainty U = 2 × u_c. For the worked glucose example U is 4.89 %, or ± 6.2 mg/dL at 126 mg/dL.

What is the formula for measurement of uncertainty from CV?

From CV alone, U = 2 × CV of long-term IQC, which ignores bias. The fuller top-down formula is U = 2 × √(CV² + RMS(bias)² + u(Cref)²), adding the bias from EQAS and the uncertainty of the assigned value. With CV 2.03 %, RMS bias 1.26 % and u(Cref) 0.5 %, U is 4.89 %.

What is the NABL formula for measurement uncertainty?

NABL publishes guidance on estimating measurement uncertainty, and labs should follow the current NABL documents applicable to medical laboratories. The top-down approach in this guide, combining IQC imprecision and EQAS bias with k = 2, is a widely used approach consistent with that guidance, but the lab chooses and documents its own method.

What is expanded uncertainty and why is k = 2?

Expanded uncertainty U is the combined standard uncertainty multiplied by a coverage factor k. With k = 2, the interval result ± U covers about 95 % of the values that could reasonably be attributed to the measurand, assuming a roughly normal distribution. It is the value usually quoted in an uncertainty statement.

How often should measurement uncertainty be recalculated?

Most labs recalculate measurement uncertainty at least yearly, and also after a change of method, analyzer or calibrator, or when QC or a lot verification shows a shift. Quarterly review is easy when the software calculates it from stored IQC and EQAS data, as PathLab Software does.

What is the difference between measurement uncertainty and total error?

Total error adds bias and imprecision linearly, for example |bias| + 1.65 × CV, and is compared with an allowable total error for QC planning. Measurement uncertainty combines components as a root sum of squares and states an interval around a result. Labs commonly use total error and Sigma for QC, and uncertainty for reporting.